yudin_2001

G. L. Yudin and M. Yu. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle”, Phys. Rev. A 64, 013409 (2001)

Source record · Catalogue · Review register

DOI: 10.1103/physreva.64.013409

Source kind: theory

Recorded technique: Analytic theory: the instantaneous (sub-cycle) ionisation rate for arbitrary Keldysh gamma in the strong-field approximation, from the Dykhne saddle-point method; the pre-exponential factor matched to the cycle-averaged PPT rate; linear and circular polarization. Atomic units (pp. 1-4).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Pages are pdf pages (1-4 = 013409-1 to -4). Identity checked against pdf p. 1.

WHY NOTHING IS TAKEN. A formula paper with no rate table: Fig. 1 (p. 3), Phi(gamma, theta)/Phi(gamma, 0) against theta for gamma = 0.25, 0.5, 1 and 2 (the dashed curve is 1/cos theta, captioned ‘the quasistatic limit gamma/cos theta << 1’); Fig. 2 (p. 3), Gamma(theta)/Gamma(0) for He at 780 nm, 5 x 10^13 W/cm^2 (gamma ~ 2), quasistatic against nonadiabatic. Text value (p. 3): at those conditions the multiphoton contribution is ‘approximately 3.3% in the total rate integrated over a half-cycle’. No quantity holds these.

KEY FORMULAS (atomic units; for review; the formulas were compared with the page images and Eq. (12) at theta = 0 reproduces the Keldysh/PPT exponent (computed 2026-09-26)): - Definitions (p. 1): gamma^2 = I_p/(2 U_p), U_p = script-E^2/(4 omega_L^2); the field script-E f(t) cos(omega_L t + phi0); phi(t) = omega_L t + phi0; n* = Z/sqrt(2 I_p), Z the ion charge. - Eq. (1), quasistatic rate (p. 1), ‘rigorously valid only in the limit gamma << 1’: Gamma_qs(t) = A_n*,l* B_l,|m| I_p (2 (2I_p)^(3/2)/(script-E f(t) |cos phi(t)|))^(2n* - |m| - 1) exp(-2 (2I_p)^(3/2)/(3 script-E f(t) |cos phi(t)|)). - Eq. (2) [8-10]: A_n*,l* = 2^(2n*)/(n* Gamma(n* + l* + 1) Gamma(n* - l*)); B_l,|m| = (2l + 1)(l + |m|)!/(2^|m| |m|! (l - |m|)!). Averaging Eq. (1) over a half-cycle gives the tunnelling formula of [8-10]. - Eq. (11) (p. 2): Gamma(t) ~ exp(-(script-E^2 f^2(t)/omega_L^3) Phi(gamma(t), theta(t))), gamma(t) = gamma/f(t); theta(t) = phi(t) - pi k, -pi/2 <= theta <= pi/2 (Eqs. (8)-(9)). - Eq. (12) (p. 2): Phi(gamma, theta) = (gamma^2 + sin^2 theta + 1/2) ln c - (3 sqrt(b - a)/(2 sqrt 2)) sin|theta| - (sqrt(b + a)/(2 sqrt 2)) gamma; a = 1 + gamma^2 - sin^2 theta; b = sqrt(a^2 + 4 gamma^2 sin^2 theta); c = sqrt((sqrt((b + a)/2) + gamma)^2 + (sqrt((b - a)/2) + sin|theta|)^2). - Eq. (13): omega_L tau_tun = -Im[arcsin(sin theta - i gamma)] (the envelope need be constant only over tau_tun). - Eq. (15), gamma >> 1: Phi ~ Phi(gamma, +-pi/2) = (gamma^2 + 3/2) ln(2 gamma) - gamma^2/2 - 1 + 35/(16 gamma^2) + ...; Eq. (16), ‘for gamma <= 2’: Phi(gamma, pi/2) ~ (4/5) gamma^2 sqrt(gamma) (1 + 3 gamma/50 - gamma^2/80), the leading term exact for gamma << 1 and within 5 % up to gamma = 1 (p. 3). - Eq. (17) (p. 3): Gamma(t) = N(t) exp(-(script-E^2 f^2(t)/omega_L^3) Phi(gamma(t), theta(t))), the sub-cycle dependence of N(t) ignored except through the envelope. - Eq. (18) (p. 4), N matched to the cycle-averaged PPT rate of [8]: N(t) = A_n*,l* B_l,|m| (3 kappa/gamma^3)^(1/2) C I_p (2 (2I_p)^(3/2)/(script-E f(t)))^(2n* - |m| - 1), kappa = ln(gamma + sqrt(gamma^2 + 1)) - gamma/sqrt(gamma^2 + 1) (this kappa is not sqrt(2 I_p)); C = (1 + gamma^2)^(|m|/2 + 3/4) A_m(omega_L, gamma), the PPT correction, A_m from Eqs. (55)-(56) of Perelomov, Popov and Terent’ev [8]; C = 1 for gamma << 1, and for gamma >> 1, m = 0, A_0 ~ 1.2/gamma^2, C ~ 1.2/sqrt(gamma) (p. 4). - Eqs. (19)-(20), circular polarization: Gamma_circ ~ exp(-(script-E^2 f^2/omega_L^3) Phi_circ(gamma)), Phi_circ = (gamma^2 + 2) cosh^-1(1 + gamma^2/2) - 2 gamma sqrt(1 + gamma^2/4).

VALIDITY AND CITED ACCURACY (p. 1): cycle-averaged tunnelling rates are accurate up to gamma ~ 0.5 [11] (Ilkov, Decker and Chin 1992: ilkov_1992); the PPT cycle-averaged formula’s accuracy ‘is excellent for many atoms (He, Ne, Ar, Kr, Xe) up to gamma = 3-4’ [12] (Larochelle, Talebpour and Chin, J. Phys. B 31, 1215 (1998)) ‘and even many small molecules’ [13] (Cornaggia and Hering, Phys. Rev. A 62, 023403 (2000)), restricted only by omega_L << omega_exc. [12] is curated as larochelle_1998 (figures only); [11] and [13] are not in the library.

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

No datasets are recorded.

Formulas

No formulas are recorded.

Corrections

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.